Dimension spectrum of Axiom A diffeomorphisms. I: The Bowen-Margulis measure

DOI10.1007/BF02187060zbMath0840.58029OpenAlexW2243323450MaRDI QIDQ1906389

Dominique Simpelaere

Publication date: 7 July 1996

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02187060

zbMATH Keywords

thermodynamic formalismlarge deviationsAxiom A diffeomorphismfree energy functionGibbs measuresmultifractalHausdorff dimensionsBowen-Margulis measure

Mathematics Subject Classification ID

Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Fractals (28A80) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Hausdorff and packing measures (28A78) Dynamical aspects of statistical mechanics (37A60)

Related Items

The correlation dimension of the Sierpinski carpet ⋮ Dimension spectrum of Axiom A diffeomorphisms. II: Gibbs measures ⋮ Tunneling in two dimensions ⋮ Critical Ising on the square lattice mixes in polynomial time ⋮ Mixing time of critical Ising model on trees is polynomial in the height ⋮ On the mixing time of the 2D stochastic Ising model with ``Plus boundary conditions at low temperature ⋮ On the two-dimensional stochastic Ising model in the phase coexistence region near the critical point ⋮ On the layering transition of an SOS surface interacting with a wall. I: Equilibrium results. ⋮ Estimates of logarithmic Sobolev constant for finite-volume continuous spin systems. ⋮ Some new results on the two-dimensional kinetic Ising model in the phase coexistence region. ⋮ Multifractal decomposition of the Sierpiński carpet.

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Geometric bounds for eigenvalues of Markov chains
• Markov chains with almost exponential hitting times
• The logarithmic Sobolev inequality for discrete spin systems on a lattice
• Correlation inequalities on some partially ordered sets
• Droplet dynamics for asymmetric Ising model
• Spectral gap and logarithmic Sobolev inequality for Kawasaki and Glauber dynamics
• Approach to equilibrium of Glauber dynamics in the one phase region. I: The attractive case
• Approach to equilibrium of Glauber dynamics in the one phase region. II: The general case
• Slow droplet-driven relaxation of stochastic Ising models in the vicinity of the phase coexistence region
• For 2-D lattice spin systems weak mixing implies strong mixing
• The droplet in the tube: A case of phase transition in the canonical ensemble
• Bound on the mass gap for finite volume stochastic Ising models at low temperature
• Shapes of growing droplets -- a model of escape from a metastable phase
• Exponential decay of connectivities in the two-dimensional Ising model
• On the asymptotics of occurrence times of rare events for stochastic spin systems.
• Renormalization group for Markov chains and application to metastability
• Polynomial-Time Approximation Algorithms for the Ising Model
• Bounds on the L 2 Spectrum for Markov Chains and Markov Processes: A Generalization of Cheeger's Inequality
• Approximating the Permanent
• Improved Bounds for Mixing Rates of Markov Chains and Multicommodity Flow

This page was built for publication: Dimension spectrum of Axiom A diffeomorphisms. I: The Bowen-Margulis measure